Chapter Demand Elasticity Chapter Outline • • • • • • The economic concept of elasticity The price elasticity of demand The cross-elasticity of demand Income elasticity Other elasticity measures Elasticity of supply Copyright ©2014 Pearson Education, Inc All rights reserved 4-2 Learning Objectives • Define and measure elasticity • Apply the concepts of price elasticity, crosselasticity, and income elasticity • Understand the determinants of elasticity • Show how elasticity affects revenue Copyright ©2014 Pearson Education, Inc All rights reserved 4-3 The Economic Concept of Elasticity • Elasticity: the percentage change in one variable relative to a percentage change in another percent change in A Elasticity  percent change in B Copyright ©2014 Pearson Education, Inc All rights reserved 4-4 Price Elasticity of Demand • Price elasticity of demand: the percentage change in quantity demanded divided by the percentage change in price % Quantity Ep  % Price Copyright ©2014 Pearson Education, Inc All rights reserved 4-5 Price Elasticity of Demand • Arc price elasticity: elasticity which is measured over a discrete interval of the demand curve Q2  Q1 P2  P1 Ep   (Q1  Q2 ) / ( P1  P2 ) / Ep = arc price elasticity Q1 = original quantity demanded Q2 = new quantity demanded P1 = original price P2 = new price Copyright ©2014 Pearson Education, Inc All rights reserved 4-6 Price Elasticity of Demand • Point elasticity: elasticity measured at a given point of a demand (or supply) curve Instead of estimating over a range of prices, it is the elasticity at a specific price The point elasticity of a linear demand function can be expressed as: Q P1 p   P Q1 Copyright ©2014 Pearson Education, Inc All rights reserved 4-7 Price Elasticity of Demand • When demand is nonlinear, the calculation of ΔQ/ΔP is somewhat more complicated because the slope of a curve changes This slope is obtained using the calculus concept of derivative In this instance, Ed= dQ/dP * P1/Q1 • The derivative of Q with respect to P (i.e., dQ/dP) is simply the instantaneous version of slope Copyright ©2014 Pearson Education, Inc All rights reserved 4-8 Price Elasticity of Demand • An example of a nonlinear demand curves is one with constant elasticity • such a curve has a nonlinear equation: Q = aP-b where b is the elasticity coefficient Copyright â2014 Pearson Education, Inc All rights reserved 4-9 Price Elasticity of Demand • Categories of elasticity • Relative elasticity of demand: Ep > • Relative inelasticity of demand: < Ep < • Unitary elasticity of demand: Ep = • Perfect elasticity: Ep = ∞ • Perfect inelasticity: Ep = Copyright ©2014 Pearson Education, Inc All rights reserved 4-10 Price Elasticity of Demand • Marginal revenue curve is twice as steep as the demand curve Copyright ©2014 Pearson Education, Inc All rights reserved 4-18 Price Elasticity of Demand • At the point where marginal revenue crosses the X-axis, the demand curve is unitary elastic and total revenue reaches a maximum Copyright ©2014 Pearson Education, Inc All rights reserved 4-19 Price Elasticity of Demand • Elasticity examples – – – – – coffee: short run -0.2, long run -0.33 kitchen and household appliances: -0.63 meals at restaurants: -2.27 airline travel in U.S.: -1.98 U.S oil demand: short run -.06, long run -.45 Copyright ©2014 Pearson Education, Inc All rights reserved 4-20 Cross-price Elasticity of Demand • Cross-price elasticity of demand: the percentage change in quantity consumed of one product as a result of a percent change in the price of a related product % Q A Ex  %PB Copyright ©2014 Pearson Education, Inc All rights reserved 4-21 Cross-price Elasticity of Demand • Arc cross-elasticity-relates the percentage change in quantity to the percentage change in the price of another product (either a substitute or a complement) Q2 A  Q1 A P2 B  P1B EX   (Q1 A  Q2 A ) / ( P1B  P2 B ) / Copyright ©2014 Pearson Education, Inc All rights reserved 4-22 Cross-price Elasticity of Demand • The sign of cross-elasticity for substitutes is positive – The sign of cross-elasticity for complements is negative – Two products are considered good substitutes or complements when the coefficient is larger than 0.5 (in ab value) Copyright ©2014 Pearson Education, Inc All rights reserved 4-23 Cross-price Elasticity of Demand • Cross-price elasticity of demand examples: – Residential demand for electric energy with respect to prices of gas energy was low, about +0.13 – The cross-elasticity of demand for beef with respect to pork prices was calculated to be about +0.25 With respect to prices of chicken, it was about +0.12 Both numbers indicate that the products are substitutes Copyright ©2014 Pearson Education, Inc All rights reserved 4-24 Income Elasticity • Income elasticity of demand: the percentage change in quantity demanded caused by a percent change in income %Q EY  % Y (Y is shorthand for income) Copyright ©2014 Pearson Education, Inc All rights reserved 4-25 Income Elasticity • Categories of income elasticity – superior goods: EY > – normal goods: ≤ EY ≤ – inferior goods: EY < Copyright ©2014 Pearson Education, Inc All rights reserved 4-26 Income Elasticity • Income elasticity examples – Short-run income elasticity for food expenditure is about 0.5 and the elasticity of restaurant meals 1.6 – The short-run income elasticity for jewelry and watches appeared to be 1.0, long run is 1.6 – For gasoline the short-run income elasticity is between 0.35 and 0.55, long run between 1.1 and 1.3 Copyright ©2014 Pearson Education, Inc All rights reserved 4-27 Other Demand Elasticity • Elasticity is encountered every time a change in some variable affects demand such as: – advertising expenditures – interest rates – population size Copyright ©2014 Pearson Education, Inc All rights reserved 4-28 Elasticity of Supply • Price elasticity of supply: the percentage change in quantity supplied as a result of a percent change in price % Quantity Supplied ES  % Price The coefficient of supply elasticity is a normally a positive number Copyright ©2014 Pearson Education, Inc All rights reserved 4-29 Elasticity of Supply • When the supply curve is more elastic, the effect of a change in demand will be greater on quantity than on the price of the product • When the supply curve is less elastic, a change in demand will have a greater effect on price than on quantity Copyright ©2014 Pearson Education, Inc All rights reserved 4-30 Global Application There are substantial differences in elasticities around the world Copyright ©2014 Pearson Education, Inc All rights reserved 4-31 Summary • Elasticity is defined as the sensitivity of one variable to another • Price elasticity of demand is the percentage change in the quantity demanded of a product caused by a percentage change in its own price • When demand is elastic, revenue rises as quantity demanded increases; revenue reaches its peak at the point of unitary elasticity and descends as quantity rises on the demand curve’s inelastic sector • Cross-price elasticity, the relationship between the demand for one product and the price of another • Income elasticity, measures the sensitivity of demand for a product to changes in the income of the population Copyright ©2014 Pearson Education, Inc All rights reserved 4-32 ... Price Elasticity of Demand • Derived demand: the demand for items that go into the production of a final commodity, such as materials, machinery, and labor – The demand for such components of... demand – The demand for such a product or factor exists because there is demand for the final product Copyright ©2014 Pearson Education, Inc All rights reserved 4-12 Price Elasticity of Demand... of Demand • Cross-price elasticity of demand examples: – Residential demand for electric energy with respect to prices of gas energy was low, about +0.13 – The cross-elasticity of demand for beef